On the Lebesgue-Nagell equation and related subjects
Barros, Carlos Filipe (2010) On the Lebesgue-Nagell equation and related subjects. PhD thesis, University of Warwick.Full text not available from this repository.
Official URL: http://webcat.warwick.ac.uk/record=b2490685~S15
The work of Cohn [Coh93] and Bugeaud, Mignotte and Siksek [BMS06] solves the Lebesgue-Naguel equation x2 + D = yn, x, y integers, n ≥ 3 for D a integer in the range 1 ≤ D ≤ 100. We propose to do the same for D in the range -100 ≤ D ≤ -1. For that we will use techniques that go from the most classical ones, ideal factorization over number fields and Thue equations, to the most modern approach to Diophantine equations, Frey curves and the Modular approach, passing by linear forms in logarithms.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||Q Science > QA Mathematics|
|Library of Congress Subject Headings (LCSH):||Number theory, Factorization (Mathematics)|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Sponsors:||Fundação para a Ciência e a Tecnologia (FCT) (SFRH/BD/29433/2006)|
|Extent:||xiii, 292 leaves|
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